Identifying symmetries and predicting cluster synchronization in complex networks

Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing symmetry group of require very high computational costs, and therefore they are hard, or even impossible, execution large sized graphs. We here unveil that there is direct connection between elements eigen-vector centrality clusters network. This gives fresh framework cluster analysis undirected connected graphs, whose cost linear $N$. show identification perfect agreement with based analyses, it allows predicting sequence synchronized which form before eventual occurrence global synchronization.